1964 Dodge Dart 270 Slant Six Restoration

Likely it has an aftermarket sending unit as your description fits. They are all crap.
Speedo, you saying if you spin the cable it works but in when connected to the transmission it does not? The speedo gear in the transmission may be installed incorrectly. In the FSM you will see the housing that hold the gear can be installed in 4 positions and depending on the number of teeth on the gear (set by rear axle ratio) the housing is rotated to a particular place. If wrong the gear can be pulled away from the drive gear and they don't mesh.

I've gotten sick of the speedometer not working so i took a look at some of it. Where it connects behind the dash, i removed the cable. I spun up the thing to make sure it works, and sure enough, it does. As soon as I put the cable in and tighten it down, the speedometer gets stuck at 7mph. That's what it was at when I purchased it, and where it gets stuck everytime the speedo cable comes out and goes back in. I'll try to see if it's something wrong with where it's attached at the transmission today or sometime this week. It doesn't make sense to me that it's always stuck at 7mph. Perhaps it just needs a small amount of oil when i insert it? I see that the FSM suggests putting a dab of 10W oil on the side that goes into the transmission.